National Borders (Still) Matter

Author

Affiliation

David Sneddon

Old Dominion University

Introduction

The gravity model of international trade. A relatively intuitive and straightforward understanding of international trade. At it’s most basic level, trade between two entities will increase with their size and decrease with their distance from each other. It is so intuitive that it is sometimes called the naïve gravity model. (Baier and Standaert 2020)

\[ X_{ij}=\beta_0Y^{\beta_{1}}_{i}Y^{\beta_{2}}_{j}dist^{\beta_{3}}_{ij}\varepsilon_{ij} \]

Or:

\[ ln(X_{ij}) = \beta_0 + \beta_1ln(Y_i)+\beta_2ln(Y_j)+\beta_3ln(dist_{ij})+ln(\varepsilon_{ij}) \]

“Where \(X_{ij}\) is is bilateral trade between exporting country \(i\) and importing country \(j\), \(Y_i(Y_j)\) is the gross domestic product in country \(i(j)\) and \(dist_{ij}\) is the bilateral distance between country \(i\) and \(j\). \(\varepsilon_{ij}\) is typically assumed to be a log-normally distributed error term.” (Baier and Standaert 2020)

I will attempt to recreate, with some modifications, the work done by John McCallum “National Borders Matter: Canada-U.S. Regional Trade Patterns” (McCallum 1995). McCallum’s article published one year after the North American Free Trade Agreement (NAFTA) came into effect. However his analysis uses data from 1988, before NAFTA came into effect.

The results of McCallum’s analysis indicated that the international border significantly diluted the effects of the gravity model, however given that NAFTA had not yet come into effect, this is intuitive. I hope to assess the effect of NAFTA by replicating McCallum’s analysis for 2019 data, the last full year that NAFTA was in effect. This year also is the last full year before significant impacts of the COVID-19 pandemic were felt in North America.

As NAFTA was designed to remove trade barriers in North America, the intuitive expectation is that the effect of the international border between Canada and the United States will be reduced, and the its effect on the naïve gravity model will be reduced.

Literature Review

This paper aims to be an only slightly modified recreation of McCallum’s work in principle. His paper forms the basis of the project. While intuition may suggest that the removal of trade barriers combined with the historically porous US-Canada border would see McCallum concluded that the effects would be modest and/or gradual. (McCallum 1995)

However, it remains clear that international trade has increased significantly, owing to decreased transport costs and a general trend of lower tariffs. (Lavallée and Vicard 2013) Nevertheless, there are other trade barriers aside from tariffs such as differences in preferences, institutions, currency differences, etc. (Anderson and Wincoop 2003)

The literature suggests that while the gravity model overall tends to hold, ceteris paribus, free trade is but one of many factors influencing trade flows across international borders.

Data

There is a wealth of data available from the Canadian government. This includes interprovincial trade amongst the Canadian provinces and even international trade between Canadian provinces and US States in addition to provinicial GDP data. Much of the US data is available from the US Census bureau, including state GDP and population.

Geographic data for Canada was more difficult to come by, as I diverged from the original work done by McCallum by using population centroids as opposed to distance to principal cities. The US population centers were available from the Census bureau, however the Canadian counterparts were not. I ended up using ChatGPT to calculate these centroids (noted in the code). Summary statistics for the data to be used in the model are listed below both with and without a logarithmic transformation.

Code Walkthrough

This project is being compiled using Quarto in RStudio. Not only does Quarto allow for professional and polished looking content; Quarto, RStudio, and R are “free”. There is a learning curve, so opportunity costs will apply. Another advantage of Quarto is the ability to embed and share code chunks in the final product. To that end: I will walk through the processes, step by step.

The entire project including all downloaded *.csv files are available on GitHub.

Alternatively you can clone the repository via CLI:

git clone https://github.com/dasneddon/local_bias.git

Libraries and Options

These are the various libraries used throughout the project.

library(readr)
library(geosphere)
library(utf8)
library(statcanR)
library(bea.R)
library(censusapi)
library(ggplot2)
library(sf)
library(rnaturalearth)
library(rnaturalearthdata)
library(canadianmaps)
library(plyr)
library(stringr)
library(usmap)
library(spData) 
library(tools)
library(modelsummary)
library(AER)
options("modelsummary_factory_default" = "kableExtra")
options(scipen = 999)

Functions

I have created a function called gravitymap() for generating the map visualizations in the appendix.

gravitymap <- function (x){
  theme_set(theme_bw())
  sf_use_s2(FALSE)
  
  worldz <- ne_countries(scale = "large", returnclass = "sf")
  class(worldz)
  (sites <- data.frame(longitude = c(-172.54, -47.74), latitude = c(23.81,
                                                                    90)))
  
  
  (sites <- st_as_sf(geodata, coords = c("lon", "lat"),
                     crs=4369, agr = "constant"))
  
  sites <- st_transform(sites, st_crs("ESRI:102010"))
  states <- st_transform(us_states, st_crs("ESRI:102010"))
  provs <- st_sf(PROV[,c(5, 10, 11, 12)])
  ak <- st_transform(alaska, st_crs("ESRI:102010"))
  hi <- st_transform(hawaii, st_crs("ESRI:102010"))
  akhi <- rbind(ak,hi)
  akhi <- cbind(akhi, st_coordinates(st_centroid(akhi)))
  akhi <- st_sf(akhi[c(2,7,8,9)])
  provs <- st_transform(provs, st_crs("ESRI:102010"))
  states <- cbind(states, st_coordinates(st_centroid(states)))
  states <- states[c(2, 7, 8, 9)]
  colnames(provs) <- colnames(akhi) <- colnames(states)
  stpr <- st_sf(rbind(as.data.frame(states),
                      as.data.frame(provs),
                      as.data.frame(akhi)))
  tf <- data.frame(us_ca_split[x])
  prov_abr2 <- prov_abr
  colnames(prov_abr2) <- colnames(st_abbr)
  tabrs <- rbind(st_abbr, prov_abr2)
  colnames(tabrs)[1] <- "NAME"
  colnames(tf) <- colnames(us_ca)
  tf$value <- log(tf$value)
  tf <- tf[c(2, 7)]
  colnames(tf)[1] <- "State"
  tstpr <- merge(stpr, tabrs, by = "NAME")
  tstpr <- merge(tstpr, tf, by = "State")
  ggplot(data = worldz) +
    geom_sf() +
    ggtitle(paste("Import Gravity Map for", prov_abr[prov_abr$from==x,])) +
    geom_sf(data = tstpr, 
            aes(fill =value)) +
    scale_fill_gradient(low="red", high= "green") +
    coord_sf(xlim = c(-6500000, 3800000), 
             ylim = c(4700000, -1700000), 
             expand = FALSE, 
             crs = st_crs("ESRI:102010"))

}

Data Imports

#DATA IMPORTS
url_df <- read.csv("url_df.csv")
usfips <- read.csv("https://www2.census.gov/geo/docs/reference/state.txt",
                   sep = "|")
usfips <- usfips[c(1, 2)]
colnames(usfips) <- c("STATE", "state")

##GEOGRAPHIC DATA
###Centers of Population
st_lat_long <- read_csv("st_pop_center.csv") #From Census.gov - 2020
canprov <- read_csv("canprovcenter.csv") #Calculated with ChatGPT - 2021
st_abbr <- read_csv("st_abbr.csv")



#DISTANCE DATA
geodata <- as.data.frame(rbind(as.matrix(st_lat_long),
                               as.matrix(canprov)))
geoframe <- data.frame(matrix(0, nrow(geodata)^2, 3))
colnames(geoframe) <- c("from", "to", "km")
c <- 1
for (i in geodata[,1]){
  for (w in geodata[,1]){
    
    lat_a <- as.numeric(geodata[geodata$state==i,2])
    lat_b <- as.numeric(geodata[geodata$state==w,2])
    lon_a <- as.numeric(geodata[geodata$state==i,3])
    lon_b <- as.numeric(geodata[geodata$state==w,3])
    geoframe[c,1] <- i
    geoframe[c,2] <- w
    geoframe[c,3] <- as.numeric(distHaversine(c(lon_a, lat_a),
                                              c(lon_b, lat_b)))/1000
    c <- c+1
  }
}
geoframe["fttag"] <- paste0(geoframe$from,geoframe$to)
geoframe <- geoframe[,c(3, 4)]




##CANADIAN DATA
can_exports <- read.csv(url_df$candata)
can_exports <- can_exports[,c(2, 4, 5, 12)]
#DATAFRAME FOR US STATE AND PROVINCIAL ABBREVIATIONS FOR UNIFORMITY
#NEEDED FOR MERGING
prov_abr <- data.frame(GEO = unique(can_exports$GEO))
prov_abr["from"] <- c("NL", "PE", "NS", "NB", "QC", "ON", "MB", "SK", "AB", 
                      "BC", "YT", "NT", "NU")
provto_abr <- prov_abr
provto_abr$GEO <- paste("To", prov_abr$GEO)
colnames(provto_abr) <- c("To_GEO","to")
colnames(can_exports)[2] <- "To_GEO"
#FORMAT can_exports  FOR MERGING
can_exports <- merge(can_exports, prov_abr, by="GEO")
can_exports <- merge(can_exports, provto_abr, by="To_GEO")
rm(provto_abr)
can_exports["value"] <- can_exports$VALUE*1000
can_exports <- can_exports[,-(1:4)]
can_exports["fttag"] <- paste0(can_exports$from,can_exports$to)
can_exports["intra"] <- -1
for (i in 1:nrow(can_exports)){
  if(can_exports$from[i]==can_exports$to[i]){
    can_exports$intra[i] <- 1
  }else
    can_exports$intra[i] <- 0
}
can_exports <- can_exports[can_exports$intra == 0,]
can_exports$intra <- NULL
tmp <- can_exports
can_exports <- tmp[,c(2,1,3,4)]
rm(tmp)
can_exports["domestic"] <- 1


###IMPORT AGGREGATE AND CONDENSE CAN_IMPORTS DATAFRAME
can_imports <- read.csv("ODPFN022_201912N.csv")
can_imports <- can_imports[can_imports$Country.Pays=="US",]
colnames(can_imports) <- c("YearMonth", 
                           "HS2", 
                           "Country", 
                           "Province", 
                           "State", 
                           "Value")
can_imports <- aggregate(can_imports$Value
                         ~ can_imports$Country
                         + can_imports$Province
                         + can_imports$State,
                         FUN = sum)
for (i in 1:nrow(can_imports)){
  for (u in 1:3){
    can_imports[i,u] <- as_utf8(can_imports[i,u])
  }
}
can_imports <- can_imports[,c(2, 3, 4)]
colnames(can_imports) <- c("to", "from", "value")
can_imports["fttag"] <- paste0(can_imports$from,can_imports$to)
can_imports["domestic"] <- 0

###CANADIAN GDP
can_gdp <- read.csv(url_df$can_gdp)
can_gdp <- can_gdp[,c("GEO","VALUE")]
can_gdp <- merge(can_gdp, prov_abr, by="GEO")
cagdp_f <- data.frame(from=can_gdp$from,
                      from_gdp=can_gdp$VALUE)
cagdp_t <- data.frame(to=can_gdp$from,
                      to_gdp=can_gdp$VALUE)
##MERGE CANADIAN IMPORTS AND EXPORTS

##US DATA
bkey <- "EB73777D-FF2C-43F1-A94A-E1BFFBA2744D"

userSpecList <- list('UserID' = bkey,
                     'Method' = 'GetData',
                     'datasetname' = 'Regional',
                     'GeoFips' = 'STATE',
                     'LineCode' = '3',
                     'TableName' = 'SAGDP1',
                     'Year' = '2019')
us_gdp <- beaGet(userSpecList)
us_gdp <- us_gdp[-1,]
us_gdp <- us_gdp[-(52:59),]
us_gdp <- us_gdp[,c(3, 6)]
exch_usca <- 1.3269 #USD TO CAD 2019 https://www.bankofcanada.ca/rates/exchange/annual-average-exchange-rates/
us_gdp <- merge(us_gdp, st_abbr, by="GeoName")
usgdp_f <- data.frame(from=us_gdp$State,
                      from_gdp=as.numeric(us_gdp$`DataValue_2019`)*exch_usca)
usgdp_t <- data.frame(to=us_gdp$State,
                      to_gdp=as.numeric(us_gdp$`DataValue_2019`)*exch_usca)
rm(us_gdp, exch_usca)
#MERGE BOTH COUNTRIES GDPs
gdp_f <- rbind(cagdp_f,usgdp_f)
rm(cagdp_f, usgdp_f)
gdp_t <- rbind(cagdp_t,usgdp_t)
rm(cagdp_t, usgdp_t)
##POPULATION
###US
st_pop <- getCensus(
  name = "dec/dhc",
  vars = "P1_001N",
  region = "state:*",
  vintage = 2020
)
st_pop$state <- as.numeric(st_pop$state)
colnames(st_pop) <- c("STATE", "pop")
st_pop <- merge(st_pop, usfips, by="STATE")
st_pop <- st_pop[,c(3, 2)]
st_pop_from <- data.frame(st_pop$state, st_pop$pop)
st_pop_to <- data.frame(st_pop$state, st_pop$pop)
colnames(st_pop_from) <- c("from","from_pop")
colnames(st_pop_to) <- c("to","to_pop")

###CANADA

prov_pop <- read.csv("prov_pop.csv")
prov_pop <- prov_pop[prov_pop$CHARACTERISTIC_ID==1 
                     & prov_pop$ALT_GEO_CODE !=  1, c(5, 12)]
colnames(prov_pop) <- c("GEO", "pop")
prov_pop <- merge(prov_pop, prov_abr, by="GEO")
prov_pop$to <- prov_pop$from
prov_pop_from <- data.frame(prov_pop$from, prov_pop$pop)
prov_pop_to <- data.frame(prov_pop$to, prov_pop$pop)
colnames(prov_pop_from) <- c("from","from_pop")
colnames(prov_pop_to) <- c("to","to_pop")

pop_from <- rbind(st_pop_from,prov_pop_from)
pop_to <- rbind(st_pop_to,prov_pop_to)
#PULL TOGETHER can_exports, can_imports, geoframe, populations, and GDPs
us_ca <- rbind(can_imports, can_exports)
us_ca <- merge(us_ca, geoframe, by = "fttag")
us_ca <- merge(us_ca, gdp_f, by = "from")
us_ca <- merge(us_ca, gdp_t, by = "to")
us_ca <- us_ca[,c(2,1,7,8,5,6,4)]
us_ca <- us_ca <- merge(us_ca, pop_from, by = "from")
us_ca <- us_ca <- merge(us_ca, pop_to, by = "to")
us_ca <- us_ca[us_ca$value != 0,]
us_ca <- us_ca[us_ca$to != "NU" & us_ca$to != "NT" & us_ca$to != "YT" &
                 us_ca$from != "NU" & us_ca$from != "NT" & us_ca$from != "YT",]
#SPLIT TO EACH PROVINCE
us_ca_split <- split(us_ca, list(us_ca$to))
#REGRESSION

coefnames <- c("Intercept","From GDP", "To GDP", "Distance (km)", "Intl. Dummy" )

reg1 <- lm(log(value[domestic==1])
           ~ log(from_gdp[domestic==1])
           + log(to_gdp[domestic==1])
           + log(km[domestic==1])
           + domestic[domestic==1],
           data = us_ca)
names(reg1$coefficients) <- coefnames

reg2 <- lm(log(value)
           ~ log(from_gdp)
           + log(to_gdp) 
           + log(km) 
           + domestic, 
           data=us_ca)

names(reg2$coefficients) <- coefnames

reg3 <- lm(log(value[(from_gdp > 10^4) & (to_gdp > 10^4)])
           ~ log(from_gdp[(from_gdp > 10^4) & (to_gdp > 10^4)])
           + log(to_gdp[(from_gdp > 10^4) & (to_gdp > 10^4)]) 
           + log(km[(from_gdp > 10^4) & (to_gdp > 10^4)]) 
           + domestic[(from_gdp > 10^4) & (to_gdp > 10^4)], 
           data=us_ca)

names(reg3$coefficients) <- coefnames

reg4 <- lm(log(value)
           ~ log(from_gdp)
           + log(to_gdp) 
           + log(km) 
           + domestic, 
           data=us_ca,
           weights = from_gdp + to_gdp)

names(reg4$coefficients) <- coefnames


reg5 <- lm(log(value)
           ~ log(from_pop)
           + log(to_pop) 
           + log(km) 
           + domestic, 
           data=us_ca)

names(reg5$coefficients) <- coefnames

reg6 <- lm(log(value)
           ~ log(from_gdp)
           + log(to_gdp) 
           + log(km), 
           data=us_ca)

names(reg6$coefficients) <- coefnames[1:4]

regz <- list(reg1, reg2, reg3, reg4, reg5, reg6)

plot ((us_ca$km), log(us_ca$value),
      pch = 20,
      cex = 1,
      main = "Distance vs Total Goods Imports",
      xlab = "Distance (km)",
      ylab = "log(Goods Imports)",
      col = alpha(us_ca$domestic+2,0.5),
      las = 1
      )
legend("topright",
       pch = 20,
       bty = "n",
       cex = 0.75,
       horiz = FALSE,
       legend = c("International", "Interprovincial"),
       col = c(2, 3))


title <- "US Canada Trade Data"
frmla <- (`Imports` = value) +
  (`Distance (km)` = km) + 
  (`Export GDP` = from_gdp) +
  (`Import GDP` = to_gdp) ~ 
  (`N` = length) + 
  Mean + 
  (`St. Dev.` = sd) + 
  (`Min` = min) + 
  (`Max` = max)
frmlalog <- (`Imports` = log(value)) +
  (`Distance (km)` = log(km)) + 
  (`Export GDP` = log(from_gdp)) +
  (`Import GDP` = log(to_gdp)) ~ 
  (`N` = length) + 
  Mean + 
  (`St. Dev.` = sd) + 
  (`Min` = min) + 
  (`Max` = max)
#Output tables
datasummary(frmla, 
            data = us_ca, 
            title = paste(title, "- Summary Statistics"),
            fmt = fmt_significant(2))
datasummary(frmlalog, 
            data = us_ca, 
            title = paste(title, "- Summary Statistics - log"), 
            fmt = fmt_significant(2))
modelsummary(regz, 
             data = us_ca, 
             title = paste(title, "- Regression"),
             fmt = fmt_significant(2))

US Canada Trade Data - Summary Statistics

	N	Mean	St. Dev.	Min	Max
Imports	580	819851002	2556957722	67	27905413372
Distance (km)	580	2298	1296	134	8678
Export GDP	580	519082	682862	6778	4071765
Import GDP	580	221674	252042	6778	833629

US Canada Trade Data - Summary Statistics - log

	N	Mean	St. Dev.	Min	Max
Imports	580	17	3.8	4.2	24
Distance (km)	580	7.6	0.67	4.9	9.1
Export GDP	580	13	1.2	8.8	15
Import GDP	580	12	1.4	8.8	14

US Canada Trade Data - Regression

	(1)	(2)	(3)	(4)	(5)	(6)
Intercept	6.48	−5.2	−3.8	−9.1	−17	3.8
	(0.86)	(1.8)	(2.1)	(1.7)	(2)	(2.0)
From GDP	0.984	1.196	1.186	1.231	1.322	0.701
	(0.046)	(0.086)	(0.095)	(0.073)	(0.086)	(0.094)
To GDP	0.935	1.694	1.631	1.698	1.799	1.637
	(0.046)	(0.069)	(0.088)	(0.061)	(0.071)	(0.081)
Distance (km)	−1.168	−1.68	−1.74	−1.24	−1.63	−1.88
	(0.074)	(0.14)	(0.16)	(0.13)	(0.14)	(0.17)
Intl. Dummy		4.34	4.1	3.8	4.00
		(0.28)	(0.3)	(0.3)	(0.26)
Num.Obs.	90	580	521	580	580	580
R2	0.908	0.656	0.604	0.678	0.673	0.513
R2 Adj.	0.905	0.654	0.600	0.675	0.671	0.511
AIC		22614.7		24150.6	22585.8	22814.2
BIC		22640.9		24176.8	22612.0	22836.0
Log.Lik.	−80.090	−1291.561	−1165.818	−1319.909	−1277.117	−1392.286
RMSE	0.59	2.24	2.27	2.28	2.19	2.67

Plot

Empirical Model

\[ln(\hat{X}_{ij})=\beta_0 + \beta_1ln(Y_{i}) + \beta_2ln(Y_{j}) + \beta_3ln(dist_{ij}) + \beta_4\delta_{ij} + ln(\varepsilon_{ij}) \] Where \(log(\hat{X}_{ij})\) is the estimated imports, \(Y_{i}\) is the GDP of the exporting province or state, \(Y_{j}\) is the GDP of the importing province, \(dist_{ij}\) is the distance in kilometers from each province or states population center, and \(\delta_{ij}\) is a dummy variable for whether the trade crosses an international border.

Note that the 5th regression in the summary statistics uses population in lieu of GDP.

I used \(log-log\) regression as there are extreme variances in the data where states with exceptionally high GDP’s such as Texas, while being one of the most distant states from the Canadian border still has a significant amount of exports. Using logarithms stabilizes this effect.

There are six variations of the regresson:
1. Canada Only
2. Canada and USA
3. Canada and USA with GDP greater that $10 billion
4. Canada and USA weighted by GDP
5. Canada and USA with population in lieu of GDP
6. Canada and USA using the naïve gravity model

Results

Discuss the results of your analysis. Interpret the coefficients.

2 + 2

Output

[1] 4

Conclusion

Remind the reader of your topic, why it is important, and what you find. Be sure to include a discussion of the implications of your findings.

Marc Bellemare has a helpful Conclusion Formula in response to Dr. Head’s.

Maps

References

Anderson, James E., and Eric van Wincoop. 2003. “Gravity with Gravitas: A Solution to the Border Puzzle.” The American Economic Review 93 (1): 170–92. http://www.jstor.org/stable/3132167.

Baier, Scott, and Samuel Standaert. 2020. “Gravity Models and Empirical Trade.” Generic. Oxford University Press. https://doi.org/10.1093/acrefore/9780190625979.013.327.

Lavallée, Emmanuelle, and Vincent Vicard. 2013. “National Borders Matter … Where One Draws the Lines Too.” Canadian Journal of Economics/Revue Canadienne d’économique 46 (1): 135–53. https://doi.org/https://doi-org.proxy.lib.odu.edu/10.1111/caje.12008.

McCallum, John. 1995. “National Borders Matter: Canada-u.s. Regional Trade Patterns.” Journal Article. The American Economic Review 85 (3): 615–23. http://www.jstor.org/stable/2118191.